Offset-fed multi-beam tracking antenna system utilizing especially shaped reflector surfaces

An antenna system for radiating and receiving electromagnetic energy at frequencies above 30 mHz comprising:

• two shaped subreflectors being generally separated, non-conic section surfaces and each separately being illuminated and fed by one or more horn radiators and one of the said shaped subreflectors with its illuminating horn radiator or horn radiators being called herein the principal feed and other shaped subreflector with illuminating horn radiator or horn radiators being called herein the secondary feed;
• and
• the principal subreflector is so shaped that electromagnetic power radiated from the said horn radiator is radiated along rays from the phase center of said horn radiator a distance r.sub.1 to the interior reflecting surface of said shaped subreflector whereupon it is reflected toward a focal point having a position determined such that the ray path r.sub.2 from the said reflector surface to the focal point F.sub.Q and the ray path continuing on from said focal point F.sub.Q to a reference paraboloid surface proximate to the said main reflector a distance .rho. such that the squared values of the ray lengths r.sub.1 r.sub.2 and .rho. obey the equation (1) ##EQU28## where in equation (1), k.sub.o is a constant and G(.theta..sub.o, .phi..sub.o) represents the power pattern of said horn radiator as a function of .theta..sub.o an angle measured from the axis of said horn radiator and of .phi..sub.o a spherical angle coordinate orthogonal to .theta..sub.o and whereby the shape of said shaped subreflector satisfies equation (1) for successive points projected along the said subreflector surface according to equation (2) which expresses Snell's Law of reflection:
• r.sub.2 =r.sub.1 -2(r.sub.1 .multidot.n)n (2)
• wherein r.sub.1, r.sub.2, and n are unit vectors lying in the direction of rays r.sub.1 and r.sub.2 and n is directed normal to said subreflector and from the unit vector n, we write
• n=a.sub.m n+b.sub.n y+c.sub.n z
• wherein a.sub.n, b.sub.n, and c.sub.n are components of vector n in directions of unit vectors x, y, z which are directed along the axis of the rectangular coordinates used to describe the said shaped subreflector and from the values a.sub.n, b.sub.n, c.sub.n, and by use of equation (3) for the partial derivative .differential.z/.differential.x and .differential.z/.differential.y ##EQU29## and whereby successive points on said shaped subreflector are located according to the numerical projector equations (4),(5),(6):
• ##EQU30##
• x.sub.i+1 =x.sub.i +.DELTA.x (5)
• y.sub.i+1 =y.sub.i ( 6)
• for x cuts across said shaped surface and ##EQU31##
• y.sub.i+1 =y.sub.i +.DELTA.y (8)
• x.sub.i+1 =x.sub.i ( 9)
• for y cuts across said shaped surface and the terms ##EQU32## are values of the partial derivatives from earlier points obtained for determining the shape of said subreflector surface;
• and
• a shaped main reflector being also generally non-conic section surface mounted in a position fixed with respect to a frame of coordinates referred to the earth's surface and said shaped main reflector being illuminated independently by said principal feed and said secondary feed such that said antenna system produces one or more antenna radiation pattern or patterns each with a main antenna beam pointed in a direction corresponding to the locations and orientations of the main shaped reflector, one of the shaped subreflectors, and one of the horn radiators;
• and
• the orientation of said shaped main reflector with respect to that of the principal feed and the secondary feed being an offset position such that electromagnetic energy radiated to and from the said principal feed and said secondary feed to illuminate said shaped main reflector is largely unobstructed and the electromagnetic energy passing to and from the shaped main reflector surface from signal sources located in directions of said antenna main beams is also largely unobstructed, said orientation of the main shaped subreflector with respect to the principal feed and the secondary feed being referred to a plane of left-right symmetry which divides the shaped main reflector surface and the two shaped subreflector surfaces into nearly equal left-right symmetric portions and such that the center of the shaped main reflector surface and the centers of the shaped subreflector surfaces, the direction of the antenna main beams all lie approximately in said plane of left-right symmetry, and the orientation of the two shaped subreflectors is such as to position one shaped subreflector above the other and such that the focal region of the main reflector lies between the said two shaped subreflectors and the shaped main reflector;
• and
• the shapes of said shaped subreflectors and said shaped main reflector being constructed to produce a prescribed electromagnetic power and phase distribution over the aperture of the shaped main reflector which distribution includes a nearly uniform power and phase aperture distribution when said shaped subreflectors and main reflector are illuminated by said horn radiators and antenna portions are oriented and positioned as specified above to produce said antenna patterns and antenna beams and
• said antenna beams being scanned in angular directions by changing the positions of said two subreflectors and their horn radiators with respect to the fixed shaped main reflector position by means of moveable supports and apparatus attached to said two shaped subreflectors and to said horn radiators such that the changed positions of the shaped subreflectors and the horn radiators enable the antenna beams to track angular changes in signal source directions.

A shaped subreflector surface illuminated by electromagnetic power from a radiator which power, upon reflection from said shaped subreflector surfaces, illuminates a main reflector and said shaped subreflector surface is so shaped that the electromagnetic power radiated from said radiator is radiated along rays from the phase center of said radiator a distance r.sub.1 to the interior reflecting surface of said shaped subreflector whereupon it is reflected toward a focal point having a position determined such that the ray path r.sub.2 from the said reflector surface to the focal point F.sub.Q and the ray path continuing on from said focal point F.sub.Q to a reference paraboloid surface proximate to the said main reflector a distance .rho. such that the squared values of the ray lengths r.sub.1, r.sub.2, and .rho. obey the equation (1) ##EQU33## where in equation (1), k.sub.o is a constant and G(.theta..sub.o, .phi..sub.o) represents the power pattern of said radiator as a function of .theta..sub.o an angle measured from the axis of said radiator and of .phi..sub.o a spherical angle coordinate orthogonal to .theta..sub.o and whereby the shape of said shaped subreflector satisfies equation (1) for successive points projected along the said subreflector surface by calculating normal vectors to the said subreflector surface according to equation (2) which expresses Snell's Law of reflection:

• r.sub.2 =r.sub.1 -z(r.sub.1 .multidot.n)n (2)
• wherein r.sub.1, r.sub.2, and n are unit vectors lying in the direction of rays r.sub.1 and r.sub.2 and n is directed normal to said subreflector and from the unit vector n, we write
• n=a.sub.n x+b.sub.n y+c.sub.n z
• wherein a.sub.n, b.sub.n, and c.sub.n are components of vector n in directions of unit vectors x, y, z which are directed along the axis of the rectangular coordinates used to describe the said shaped subreflector and from the values a.sub.n, b.sub.n, c.sub.n, and by use of equation (3) for the partial derivative .differential.z/.differential.x and .differential.z/.differential.y ##EQU34## and whereby successive points on said shaped subreflector are located according to the numerical projector equations (4),(5),(6):
• ##EQU35##
• x.sub.i+1 =x.sub.i +.DELTA.x (5)
• y.sub.i+1 =y.sub.i ( 6)
• for x cuts across said shaped surface and ##EQU36##
• y.sub.i+1 =y.sub.i +.DELTA.y (8)
• x.sub.i+1 =x.sub.i ( 9)
• for y cuts across said shaped surface and the terms ##EQU37## are values of the partial derivatives from earlier points obtained for determining the shape of said subreflector surface.

A reflector antenna functioning in transmitting and receiving modes comprising:

• a shaped reflector and an illuminating feed wherein,
• the shape of the reflecting surface of the shaped reflector is determined by the radiation pattern of the illuminating feed such that said reflector antenna produces an antenna pattern having a main beam with antenna gain of the approximate form csc.sup.2 .theta. in a given plane where .theta. is the spherical coordinate angle in said given plane .theta. being approximately zero at the peak of said main beam and where .phi. is the spherical coordinate angle in planes orthogonal to .theta. in which plane said main beam has a narrow nearly constant angular beamwidth such that the said main beam is fan-shaped in form and when .theta. is the elevation angle plane measured from the horizon toward the zenith of a radar mounted on the surface of the earth then the radar signals transmitted and subsequently received by said reflector antenna functioning with said radar from a reflecting target flying at a constant altitude above the surface of the earth are nearly constant;
• and
• said shaped reflector being a doubly curved surface constructed by connecting points on the reflector surface determined at successive points by finding through interpolation at or near the interception points on the reflecting surface of said rays obtained from the radiation pattern of said illuminating feed and by extrapolation along the reflection surface to successive points by finding normals to and partial derivatives of the reflecting surface under construction through use of said rays and points on the reflecting surface previously determined so that the main beam of the radiation pattern produced by said reflector antenna has the approximate gain function in either the receiving or transmitting mode of csc.sup.2 .theta. in the .theta. plane and narrow angular beamwidths in said .theta. plane orthogonal to the .theta. plane and at certain values of the angle .theta. the main beam is focused to points at specified distances from the antenna to further reduce the angular beamwidths in .theta. planes of the antenna patterns.

An antenna system for radiating and receiving electromagnetic energy comprising:

• one or more shaped subreflector or subreflectors, generally not conic sections in form, each illuminated by one or more radiator or radiators;
• and each radiator together with the subreflector that it illuminates constituting separate antenna feeds, which feeds illuminate a common shaped main reflector whose central portion is tangent to a reference offset paraboloidal section and said main reflector edge contour dimensions are dependent on the radiation pattern of one of the radiators;
• and said shaped subreflector or subreflectors and their radiator or radiators are positioned and moved with their central portions lying approximately in a plane containing the central point on the shaped main reflector surface and the axis of said reference offset paraboloidal section such that the electromagnetic energy passing to and from the shaped main reflector and to and from any radiator or shaped subreflector is largely unobstructed;
• and the antenna system produces one or more radiation patterns each with a nearly circularly symmetric main beam that can be steered in direction by motions of a radiator and a subreflector;
• and the antenna gain and pattern sidelobes of one of the radiation patterns are controlled by shaping the reflecting surface of one of the shaped subreflectors and by shaping the reflecting surface of the shaped main reflector.